Question

Force on a particle is given by: F = -kx^n. For what values of n will the motion be oscillatory?

(a) 3

(b) 4

(c) Any integer

(d) It cannot be oscillatory for any value of n

This question was posed to me in an online quiz.

The above asked question is from Periodic and Oscillatory Motions topic in section Oscillations of Physics – Class 11

Answer 1

Correct option is (a) 3

To elaborate: For motion to be oscillatory there has to be an equilibrium position towards which the force is acting throughout the motion.                                                                                                                                                         In the expression, F = -kx^n,                                                                                                                                                 If n is even, force will always act in one direction.                                                                                                           If n is odd, force will change direction when x changes direction and will always act towards the origin.       Hence, motion will be oscillatory if n is odd.                                                                                                                                         Thus, from the given options 3 is correct.